Argumentação e prova na matemática escolar do ensino básico: a soma das medidas dos ângulos internos de um triângulo - Almeida, Julio Cesar Porfirio de (2007)
This study is about the demonstration of amount of measure the internal angles of triangles made by 8th grade from Fundamental School and the First year of High School, from of resolution of two specified questions. This work intends to contribute with the Argumentation and Proof in School Mathematics project (AprovaME), that has as one of objectives the mapping of conceptions about teenager s argumentation and proofs in public and private schools of São Paulo (state) For this was made a questionnaire in two books, five questions of Algebra and with five questions of Geometry. They were given to 1998 pupils aged between 14 and 16 years. The two analyzed questions are in the Geometry notebook. After checking the given information, took out 50 pupils as sample, that answers were classified in four progressive levels according their form of argument used in evolution of the Pragmatic proof (first principles methods of verification) to the Intellectual proof (elaborations of reasoning from logical-deduction nature and the production of explanation characterized as mathematics demonstration). In the following phase these pupils were put in groups according with the types of answers presented, to do the individual interviews aiming explanations about their choose. Finish the work a conclusive survey based in the results of the analysis, where are suggested forms of approach of subject Proofs and Demonstrations in the classroom, contemplating the execution of dynamic activities that give privilege the construction of mathematically consistent argument based in the expression of generalized reasoning